Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22548744 | C2 | semidirect |
| 3. C4×Q8×D251 | C2 | semidirect |
| 4. #30631908 | C2 | semidirect |
| 5. #30631907 | C2 | semidirect |
| 6. #30631898 | C2 | semidirect |
| 7. #30631897 | C2 | semidirect |
| 8. #30631884 | C2 | semidirect |
| 9. #30631709 | C2 | semidirect |
| 10. #30631685 | C2 | semidirect |
| 11. #460×C251 | C2 | semidirect |
| 50. Q8×D251 | D4 | semidirect |
| 132. C4×C251 | #137 | semidirect |
| 146. C251 | #3037 | semidirect |
| 156. #460 | D251 | semidirect |
| 285. C4 | #22548744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548744 | 2 |
| #30632235 | 2 |
| C4×Q8×D251 | 2 |
| #30631908 | 2 |
| #30631907 | 2 |
| #30631898 | 2 |
| #30631897 | 2 |
| #30631884 | 2 |
| #30631709 | 2 |
| #30631685 | 2 |
| #460×C251 | 2 |
| #3037 | 251 |